PROBLEM SET 1 - EVOLUTIONARY BIOLOGY - FALL 2016 KEY
Hardy-Castle-Weinberg (20 pts total)
1. A population of infants from Musoma, Tunisia, was scored for the β-hemoglobin locus genotype (determined
by a single autosomal locus with two alleles, A and S) as follows:
Genotype AA AS SS Total
Number 189 89 9 287
Characterize this population by its genotype frequencies. Characterize the gene pool by the allele frequencies
for A and S. Using Hardy-Weinberg Law, predict the genotype frequencies based on the allele frequencies. (3
pts)
Observed Genotype Frequencies:
Freq(AA) = 189/287 = 0.66
Freq(AS) = 89/287 = 0.31
Freq(SS) = 9/287 = 0.03
Allele Frequencies:
Freq(A) = p = 189/287 + ½(89/287) = 0.81
Freq(S) = q = 9/287 + ½(89/287) = 0.19
(Or use p + q = 1 to solve for q)
Expected HWE genotype frequencies
p2 = (0.81)2 = 0.66
2pq = 2(0.81)(0.19) = 0.3
q2 = (0.19)2 = 0.03
2. Among people of southern Italian and Sicilian ancestry living in Rochester, New York (N = 10,000), about one
birth in 2,500 has thalassemia major (a type of anemia) and about one birth in 25 has a milder anemia known
as thalassemia minor. Are these data compatible with a single locus hypothesis as a basis for the heredity of
these anemic conditions? Show why or why not. (3 pts)
To answer this question, construct a model with all the elements of the basic Hardy-Weinberg model and see
if the data you have been given fit. Assume two alleles and one locus and arbitrarily name the alleles A and a.
If you assume that thalassemia major is a homozygous genotype (AA) and that thalassemia minor is a
heterozygous genotype (Aa) then you have the genotype frequencies from the question to work with:
AA = 1/2500 = 0.0004; Aa = 1/25 = 0.04; and aa= 1-0.04-0.0004 = 0.9596
Solve for the allele frequencies:
pA= 0.0004 +1/2(0.04) = 0.0204
qa= 0.9596 + 1/2(0.04) = 0.9796
Given these values for p and q, the expected genotype frequencies under H-W are p2 = 0.0004; 2pq = 0.04;
q2 = 0.9596. These frequencies match the given values in the population. Therefore, this trait fits the H-W
two-allele, one-locus model.
3. Two populations are examined for the same gene locus with the following results:
